| public static svdcmp ( double a, double &w, double &v ) : void | ||
| a | double | |
| w | double | |
| v | double | |
| return | void | |
public static void svdcmp(double[,] a, out double[] w, out double[,] v)
{
// number of rows in A
int m = a.GetLength(0);
// number of columns in A
int n = a.GetLength(1);
if (m < n)
{
throw new ArgumentException("Number of rows in A must be greater or equal to number of columns");
}
w = new double[n];
v = new double[n, n];
int flag, i, its, j, jj, k, l = 0, nm = 0;
double anorm, c, f, g, h, s, scale, x, y, z;
double[] rv1 = new double[n];
// householder reduction to bidiagonal form
g = scale = anorm = 0.0;
for (i = 0; i < n; i++)
{
l = i + 1;
rv1[i] = scale * g;
g = s = scale = 0;
if (i < m)
{
for (k = i; k < m; k++)
{
scale += System.Math.Abs(a[k, i]);
}
if (scale != 0.0)
{
for (k = i; k < m; k++)
{
a[k, i] /= scale;
s += a[k, i] * a[k, i];
}
f = a[i, i];
g = -Sign(System.Math.Sqrt(s), f);
h = f * g - s;
a[i, i] = f - g;
if (i != n - 1)
{
for (j = l; j < n; j++)
{
for (s = 0.0, k = i; k < m; k++)
{
s += a[k, i] * a[k, j];
}
f = s / h;
for (k = i; k < m; k++)
{
a[k, j] += f * a[k, i];
}
}
}
for (k = i; k < m; k++)
{
a[k, i] *= scale;
}
}
}
w[i] = scale * g;
g = s = scale = 0.0;
if ((i < m) && (i != n - 1))
{
for (k = l; k < n; k++)
{
scale += System.Math.Abs(a[i, k]);
}
if (scale != 0.0)
{
for (k = l; k < n; k++)
{
a[i, k] /= scale;
s += a[i, k] * a[i, k];
}
f = a[i, l];
g = -Sign(System.Math.Sqrt(s), f);
h = f * g - s;
a[i, l] = f - g;
for (k = l; k < n; k++)
{
rv1[k] = a[i, k] / h;
}
if (i != m - 1)
{
for (j = l; j < m; j++)
{
for (s = 0.0, k = l; k < n; k++)
{
s += a[j, k] * a[i, k];
}
for (k = l; k < n; k++)
{
a[j, k] += s * rv1[k];
}
}
}
for (k = l; k < n; k++)
{
a[i, k] *= scale;
}
}
}
anorm = System.Math.Max(anorm, (System.Math.Abs(w[i]) + System.Math.Abs(rv1[i])));
}
// accumulation of right-hand transformations
for (i = n - 1; i >= 0; i--)
{
if (i < n - 1)
{
if (g != 0.0)
{
for (j = l; j < n; j++)
{
v[j, i] = (a[i, j] / a[i, l]) / g;
}
for (j = l; j < n; j++)
{
for (s = 0, k = l; k < n; k++)
{
s += a[i, k] * v[k, j];
}
for (k = l; k < n; k++)
{
v[k, j] += s * v[k, i];
}
}
}
for (j = l; j < n; j++)
{
v[i, j] = v[j, i] = 0;
}
}
v[i, i] = 1;
g = rv1[i];
l = i;
}
// accumulation of left-hand transformations
for (i = n - 1; i >= 0; i--)
{
l = i + 1;
g = w[i];
if (i < n - 1)
{
for (j = l; j < n; j++)
{
a[i, j] = 0.0;
}
}
if (g != 0)
{
g = 1.0 / g;
if (i != n - 1)
{
for (j = l; j < n; j++)
{
for (s = 0, k = l; k < m; k++)
{
s += a[k, i] * a[k, j];
}
f = (s / a[i, i]) * g;
for (k = i; k < m; k++)
{
a[k, j] += f * a[k, i];
}
}
}
for (j = i; j < m; j++)
{
a[j, i] *= g;
}
}
else
{
for (j = i; j < m; j++)
{
a[j, i] = 0;
}
}
++a[i, i];
}
// diagonalization of the bidiagonal form: Loop over singular values
// and over allowed iterations
for (k = n - 1; k >= 0; k--)
{
for (its = 1; its <= 30; its++)
{
flag = 1;
for (l = k; l >= 0; l--)
{
// test for splitting
nm = l - 1;
if (System.Math.Abs(rv1[l]) + anorm == anorm)
{
flag = 0;
break;
}
if (System.Math.Abs(w[nm]) + anorm == anorm)
break;
}
if (flag != 0)
{
c = 0.0;
s = 1.0;
for (i = l; i <= k; i++)
{
f = s * rv1[i];
if (System.Math.Abs(f) + anorm != anorm)
{
g = w[i];
h = Pythag(f, g);
w[i] = h;
h = 1.0 / h;
c = g * h;
s = -f * h;
for (j = 0; j < m; j++)
{
y = a[j, nm];
z = a[j, i];
a[j, nm] = y * c + z * s;
a[j, i] = z * c - y * s;
}
}
}
}
z = w[k];
if (l == k)
{
// convergence
if (z < 0.0)
{
// singular value is made nonnegative
w[k] = -z;
for (j = 0; j < n; j++)
{
v[j, k] = -v[j, k];
}
}
break;
}
if (its == 30)
{
throw new InvalidOperationException("No convergence in 30 svdcmp iterations");
}
// shift from bottom 2-by-2 minor
x = w[l];
nm = k - 1;
y = w[nm];
g = rv1[nm];
h = rv1[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
g = Pythag(f, 1.0);
f = ((x - z) * (x + z) + h * ((y / (f + Sign(g, f))) - h)) / x;
// next QR transformation
c = s = 1.0;
for (j = l; j <= nm; j++)
{
i = j + 1;
g = rv1[i];
y = w[i];
h = s * g;
g = c * g;
z = Pythag(f, h);
rv1[j] = z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = g * c - x * s;
h = y * s;
y *= c;
for (jj = 0; jj < n; jj++)
{
x = v[jj, j];
z = v[jj, i];
v[jj, j] = x * c + z * s;
v[jj, i] = z * c - x * s;
}
z = Pythag(f, h);
w[j] = z;
if (z != 0)
{
z = 1.0 / z;
c = f * z;
s = h * z;
}
f = c * g + s * y;
x = c * y - s * g;
for (jj = 0; jj < m; jj++)
{
y = a[jj, j];
z = a[jj, i];
a[jj, j] = y * c + z * s;
a[jj, i] = z * c - y * s;
}
}
rv1[l] = 0.0;
rv1[k] = f;
w[k] = x;
}
}
}
